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/* mpc_div -- Divide two complex numbers.
Copyright (C) 2002 Andreas Enge, Paul Zimmermann
This file is part of the MPC Library.
The MPC Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPC Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPC Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include "gmp.h"
#include "mpfr.h"
#include "mpc.h"
#include "mpc-impl.h"
int
mpc_div (mpc_ptr a, mpc_srcptr b, mpc_srcptr c, mp_rnd_t rnd)
{
int ok_re=0, ok_im=0;
mpc_t res, c_conj;
mpfr_t q;
mp_prec_t prec;
int inexact_prod, inexact_norm, inexact_re, inexact_im;
prec = MPC_MAX_PREC(a);
mpc_init (res);
mpfr_init (q);
/* create the conjugate of c in c_conj without allocating new memory */
MPC_RE (c_conj)[0] = MPC_RE (c)[0];
MPC_IM (c_conj)[0] = MPC_IM (c)[0];
MPFR_CHANGE_SIGN (MPC_IM (c_conj));
do
{
prec += _mpfr_ceil_log2 ((double) prec) + 5;
mpc_set_prec (res, prec);
mpfr_set_prec (q, prec);
/* first compute norm(c)^2 */
inexact_norm = mpc_norm (q, c, GMP_RNDD);
/* now compute b*conjugate(c) */
/* We need rounding away from zero for both the real and the imagin- */
/* ary part; then the final result is also rounded away from zero. */
/* The error is less than 1 ulp. Since this is not implemented in */
/* mpfr, we round towards zero and add 1 ulp to the absolute values */
/* if they are not exact. */
inexact_prod = mpc_mul (res, b, c_conj, MPC_RNDZZ);
inexact_re = MPC_INEX_RE (inexact_prod);
inexact_im = MPC_INEX_IM (inexact_prod);
if (inexact_re != 0)
mpfr_add_one_ulp (MPC_RE (res), GMP_RNDN);
if (inexact_im != 0)
mpfr_add_one_ulp (MPC_IM (res), GMP_RNDN);
/* divide the product by the norm*/
if (inexact_norm == 0 && (inexact_re == 0 || inexact_im == 0))
{
/* The divison has good chances to be exact in at least one part. */
/* Since this can cause problems when not rounding to the nearest, */
/* we use the division code of mpfr, which handles the situation. */
if (MPFR_SIGN (MPC_RE (res)) > 0)
{
inexact_re |= mpfr_div (MPC_RE (res), MPC_RE (res), q, GMP_RNDU);
ok_re = mpfr_can_round (MPC_RE (res), prec - 4, GMP_RNDU,
MPC_RND_RE(rnd), MPFR_PREC(MPC_RE(a)));
}
else
{
inexact_re |= mpfr_div (MPC_RE (res), MPC_RE (res), q, GMP_RNDD);
ok_re = mpfr_can_round (MPC_RE (res), prec - 4, GMP_RNDD,
MPC_RND_RE(rnd), MPFR_PREC(MPC_RE(a)));
}
if (ok_re || !inexact_re) /* compute imaginary part */
{
if (MPFR_SIGN (MPC_IM (res)) > 0)
{
inexact_im |= mpfr_div (MPC_IM (res), MPC_IM (res), q, GMP_RNDU);
ok_im = mpfr_can_round (MPC_IM (res), prec - 4, GMP_RNDU,
MPC_RND_IM(rnd), MPFR_PREC(MPC_IM(a)));
}
else
{
inexact_im |= mpfr_div (MPC_IM (res), MPC_IM (res), q, GMP_RNDD);
ok_im = mpfr_can_round (MPC_IM (res), prec - 4, GMP_RNDD,
MPC_RND_IM(rnd), MPFR_PREC(MPC_IM(a)));
}
}
}
else
{
/* The division is inexact, so for efficiency reasons we invert q */
/* only once and multiply by the inverse. */
/* We do not decide about the sign of the difference. */
inexact_re = 1;
inexact_im = 1;
mpfr_ui_div (q, 1, q, GMP_RNDU);
if (MPFR_SIGN (MPC_RE (res)) > 0)
{
mpfr_mul (MPC_RE (res), MPC_RE (res), q, GMP_RNDU);
ok_re = mpfr_can_round (MPC_RE (res), prec - 4, GMP_RNDU,
MPC_RND_RE(rnd), MPFR_PREC(MPC_RE(a)));
}
else
{
mpfr_mul (MPC_RE (res), MPC_RE (res), q, GMP_RNDD);
ok_re = mpfr_can_round (MPC_RE (res), prec - 4, GMP_RNDD,
MPC_RND_RE(rnd), MPFR_PREC(MPC_RE(a)));
}
if (ok_re) /* compute imaginary part */
{
if (MPFR_SIGN (MPC_IM (res)) > 0)
{
mpfr_mul (MPC_IM (res), MPC_IM (res), q, GMP_RNDU);
ok_im = mpfr_can_round (MPC_IM (res), prec - 4, GMP_RNDU,
MPC_RND_IM(rnd), MPFR_PREC(MPC_IM(a)));
}
else
{
mpfr_mul (MPC_IM (res), MPC_IM (res), q, GMP_RNDD);
ok_im = mpfr_can_round (MPC_IM (res), prec - 4, GMP_RNDD,
MPC_RND_IM(rnd), MPFR_PREC(MPC_IM(a)));
}
}
}
}
while ((!ok_re && inexact_re) || (!ok_im && inexact_im));
mpc_set (a, res, rnd);
mpc_clear (res);
mpfr_clear (q);
return (MPC_INEX (inexact_re, inexact_im));
/* Only exactness vs. inexactness is tested, not the sign. */
}
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